Calculus: l’Hôpital’s rule: another proof that lim_x→0 sinx/x = 1

The tutor shows that lim_x→0 sinx/x = 1 using l’Hôpital’s rule.

Put very simply, l’Hôpital’s rule states that for a situation where Limit f(x)/g(x) = 0/0, Limit f(x)/g(x) = Limit f'(x)/g'(x), provided f(x), g(x) are both differentiable and so on. Such is the exact premise of lim_x→0 sinx/x.

Using l’Hôpital’s rule,

lim_x→0 sinx/x = lim_x→0 (sinx)’/x’ = lim_x→0 cosx/1 = 1/1 = 1

Source:

Larson, Roland and Robert Hostetler. Calculus, 3rd ed. Toronto: D C Heath and Company, 1989.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Calculus: l’Hôpital’s rule: another proof that limx→0 sinx/x = 1

The tutor shows that limx→0 sinx/x = 1 using l’Hôpital’s rule.